Quotient space of an algebraic stack

In algebraic geometry, the quotient space of an algebraic stack F, denoted by |F|, is a topological space which as a set is the set of all integral substacks of F and which then is given a "Zariski topology": an open subset has a form

for some open substack U of F.[1] The construction

of algebraic stacks determines a continuous map

An algebraic stack X is punctual if

When X is a moduli stack, the quotient space

is called the moduli space of X.

is a morphism of algebraic stacks that induces a homeomorphism

, then Y is called a coarse moduli stack of X.

("The" coarse moduli requires a universality.)

This algebraic geometry–related article is a stub.